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''' | ||
tmd matching algorithms implementation | ||
''' | ||
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def marriage_problem(women_preferences, men_preferences): | ||
'''Matches N women to M men so that max(M, N) | ||
are coupled to their preferred choice that is available | ||
See https://en.wikipedia.org/wiki/Stable_marriage_problem | ||
''' | ||
N = len(women_preferences) | ||
M = len(men_preferences) | ||
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swapped = False | ||
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if M > N: | ||
swap = women_preferences | ||
women_preferences = men_preferences | ||
men_preferences = swap | ||
N = len(women_preferences) | ||
M = len(men_preferences) | ||
swapped = True | ||
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free_women = range(N) | ||
free_men = range(M) | ||
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couples = {x: None for x in range(N)} # woman first, then current husband | ||
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while len(free_men) > 0: | ||
m = free_men.pop() | ||
choice = men_preferences[m].pop(0) | ||
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if choice in free_women: | ||
couples[choice] = m | ||
free_women.remove(choice) | ||
else: | ||
current = np.where(np.array(women_preferences)[choice] == couples[choice])[0][0] | ||
tobe = np.where(np.array(women_preferences)[choice] == m)[0][0] | ||
if current < tobe: | ||
free_men.append(couples[choice]) | ||
couples[choice] = m | ||
else: | ||
free_men.append(m) | ||
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if swapped: | ||
return [(couples[k], k) for k in couples] | ||
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return [(k, couples[k]) for k in couples] | ||
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def symmetric(p): | ||
'''Returns the symmetric point of a PD point on the diagonal | ||
''' | ||
return [(p[0] + p[1]) / 2., (p[0] + p[1]) / 2] | ||
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def matching_diagrams(p1, p2, plot=False, method='munkres', use_diag=True, new_fig=True, subplot=(111)): | ||
'''Returns a list of matching components | ||
Possible matching methods: | ||
- munkress | ||
- marriage problem | ||
''' | ||
from scipy.spatial.distance import cdist | ||
import munkres | ||
from tmd.view import common as _cm | ||
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def plot_matching(p1, p2, indices, new_fig=True, subplot=(111)): | ||
'''Plots matching between p1, p2 | ||
for the corresponding indices | ||
''' | ||
import pylab as plt | ||
fig, ax = _cm.get_figure(new_fig=new_fig, subplot=subplot) | ||
for i, j in indices: | ||
ax.plot((p1[i][0], p2[j][0]), (p1[i][1], p2[j][1]), color='black') | ||
ax.scatter(p1[i][0], p1[i][1], c='r') | ||
ax.scatter(p2[j][0], p2[j][1], c='b') | ||
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if use_diag: | ||
p1_enh = p1 + [symmetric(i) for i in p2] | ||
p2_enh = p2 + [symmetric(i) for i in p1] | ||
else: | ||
p1_enh = p1 | ||
p2_enh = p2 | ||
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D = cdist(p1_enh, p2_enh) | ||
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if method == 'munkres': | ||
m = munkres.Munkres() | ||
indices = m.compute(np.copy(D)) | ||
elif method == 'marriage': | ||
first_pref = [np.argsort(k).tolist() for k in cdist(p1_enh, p2_enh)] | ||
second_pref = [np.argsort(k).tolist() for k in cdist(p2_enh, p1_enh)] | ||
indices = marriage_problem(first_pref, second_pref) | ||
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if plot: | ||
plot_matching(p1_enh, p2_enh, indices, new_fig=new_fig, subplot=subplot) | ||
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ssum = np.sum([D[i][j] for (i, j) in indices]) | ||
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return indices, ssum | ||
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